Non-Abelian Gauge Field Inflation

Abstract: In [arXiv:1102.1513] we introduced an inflationary scenario, Non-Abelian Gauge Field Inflation or gauge-flation for short, in which slow-roll inflation is driven by non-Abelian gauge field minimally coupled to gravity. We present a more detailed analysis, both numerical and analytical, of the gauge-flation. By studying the phase diagrams of the theory, we show that getting enough number of e-folds during a slow-roll inflation is fairly robust to the choice of initial gauge field values. In addition, we present a detailed analysis of the cosmic perturbation theory in gauge-flation which has many special and interesting features compared the standard scalar-driven inflationary models. The specific gauge-flation model we study in this paper has two parameters, a cutoff scale Lambda and the gauge coupling g. Fitting our results with the current cosmological data fixes \Lambda\sim 10 H \sim 10^{15} GeV (H is the Hubble parameter) and g\sim 10^{-4}, which are in the natural range of parameters in generic particle physics beyond standard models. Our model also predicts a tensor-to-scalar ratio r>0.05, in the range detectable by the Planck satellite.

• The paper introduces gauge-flation, a model where non-Abelian gauge fields act as inflatons, offering an alternative to traditional scalar-based inflation.
• It employs both analytical and numerical methods to demonstrate that slow-roll conditions and sufficient e-folding emerge naturally from varied initial configurations.
• The model predicts a tensor-to-scalar ratio (r) exceeding 0.02, indicating a potentially observable signature in CMB polarization experiments.

Non-Abelian Gauge Field Inflation: A Detailed Analysis

The paper "Non-Abelian Gauge Field Inflation," authored by A. Maleknejad and M. M. Sheikh-Jabbari, presents an in-depth examination of a novel inflationary model driven by non-Abelian gauge fields, a scenario referred to as gauge-flation. While traditional inflationary models typically rely on scalar fields, this research introduces a paradigm where the inflaton is constituted by a gauge field, specifically within a non-Abelian framework.

Core Contributions and Analysis

Maleknejad and Sheikh-Jabbari emphasize the possibility of achieving slow-roll inflation through non-Abelian gauge fields minimally coupled to gravity. The model, referred to as gauge-flation, is studied both analytically and numerically, showcasing robust slow-roll inflation dynamics across a variety of initial gauge field configurations.

Key Theoretical Insights

1. Gauge Field Configuration and Symmetry: The paper crucially maintains rotational symmetry by leveraging the $SU(2)$ subgroup of the gauge symmetry. By aligning the global part of the non-Abelian gauge symmetry group with spatial rotations, the authors ensure isotropy and homogeneity in a Friedmann-Robertson-Walker (FRW) cosmological setting. This alignment is pivotal, allowing gauge fields, inherently non-scalar, to serve as inflaton candidates without violating symmetry constraints traditionally upheld in scalar-driven models.
2. Action Construction: The gauge-flation model is meticulously constructed using an action comprising a Yang-Mills term supplemented by a $F^4$ interaction term, expressed as $$(\epsilon^{\mu\nu\lambda\sigma}F^a_{\mu\nu}F^a_{\lambda\sigma})^2$$. This specific configuration is chosen to overcome the rapid decay and suppression issues typically associated with vector fields in an inflationary background.
3. Slow-roll Dynamics: Analytic treatment of the model reveals conditions under which slow-roll inflation occurs, mainly when the $F^4$ term contribution dominates over the Yang-Mills component. The robustness of slow-roll to initial conditions is numerically validated, demonstrating the model's natural capability to yield sufficient e-folds for cosmological expansion.

Numerical Results and Predictions

Through comprehensive numerical simulations, Maleknejad and Sheikh-Jabbari illustrate that gauge-flation furnishes inflationary trajectories yielding adequate e-folding and with relatively weak dependence on the fine-tuning of initial conditions. These simulations highlight a tensor-to-scalar ratio $r>0.02$, a value within the detection range of the Planck satellite, thus indicating a potentially observable signature of gauge-flation in cosmic microwave background (CMB) anisotropies.

Implications and Future Prospects

The gauge-flation model harbors significant implications both for theoretical physics and cosmological observations:

• Theoretical Advancement: This model innovatively situates gauge fields as inflatons, extending the landscape of inflationary models beyond scalar field dominance. It further elucidates the role of gauge symmetries in preserving isotropy and homogeneity in cosmological scenarios.
• Observational Opportunities: With model parameters fitting within current cosmological constraints, notably predictions on $r$, future satellite missions focused on CMB polarization could empirically validate or refute the gauge-flation model.
• Applications in Particle Physics: The alignment of the gauge coupling and cutoff scales with naturally occurring values in particle physics may provide a fertile ground for embedding inflation within larger frameworks like supersymmetric grand unified theories (SUSY GUTs).

Conclusion

Maleknejad and Sheikh-Jabbari's exploration into gauge-flation presents a compelling alternative to traditional scalar-based inflation models, positioned excellently within theoretical and observational bounds. The model not only underscores the versatility of non-Abelian gauge fields but also paves the way for deeper exploration into the intertwining avenues of cosmology and high-energy particle physics, potentially influencing the course of future research and technological developments in the field of cosmic inflation.